The correct view of the Gospel is it is the entire content of what the apostles taught and preached, and the Church still teaches today
The apostles were the first ones to receive the entire Gospel. That is, they were constantly taught by Jesus for 3 years. Only parts of these teachings were written in the Gospels. Then they were taught by Jesus after He died, but before His resurrection. In Acts, it says Jesus taught them about the kingdom. None of this is written explicitly anywhere in scripture. Then Jesus sent them the Holy Spirit to teach them all things:
Joh 14:26 “But the Counselor, the
Holy Spirit, whom the Father will
send in my name, he will teach
you all things…”
None of this is written explicitly in the bible. Thus, the vast majority of the teachings the apostles knew were not explicitly written at all.
But our salvation depends on knowing this Gospel.
Jesus said:
"Go into all the world and preach the gospel
to the whole creation.
16 He who believes and is baptized
will be saved; but he who does not
believe will be condemned. (Mark 16:15)
So how do we know what this Gospel is since it was never written down?
Even an athiest can know. Just learn what the early Christian writers said they learned from the apostles. Read what the fathers of the Church said they learned from the apostles. As anyone who studies these writings knows, these teachings they learned from the apostles are the same teachings of the Church today. The Church today got her basic teachings on Mary being our mother, on pugatory,on contraception, on mortal and venial sin, on grace, on prayer to the saints, on the moral teachings of the Church, especially sexual morality, on the basics of salvation, on the fundamental hierarchy of truths, the creed, sacraments, commandments and prayer, etc, from the Gospel the apostles taught and preached.
There is nothing the early Christians learned from the apostles that the Church does not teach today. There is nothing the Church teaches today that the early Christians did not know, or that follows from what they knew. The exact same Gospel they believed is the exact same Gospel the Church teaches today. So when the Church teaches the faith, the Church is teaching the Gospel, the same Gospel that the apostles taught.
The apostles taught and preached their Gospel in an organized and systamatic way, otherwise the ordinary lay people could never remember it or understand it. They taught it usually in the form of explaining the history of salvation, based on the scriptures, then the arcticles of the creed, the sacraments, the commandments and prayer. Sometimes they combined the commandments and prayer, or other combinations. But the content was exactly the same as the content we know today, no matter what form they used. The reason they used the form of the creed, sacraments, commandments and prayer is because these are part of the hierarchy of truths, this is because “some truths are based on others as of a higher priority and are illumined by them” (General Directory for Catechesis). Thus, we can’t teach about how we receive the salvation won by Jesus without teaching the sacraments. We can’t teach about how we love God and neighbor without teaching the commandments, we can’t teach about how we turn to God without the teaching on prayer. We can’t teach who Jesus is, who God is, why He created us, why He came into the world, etc, without teaching the basics of the creed.
The entire Gospel the apostles taught is ordered around these hierarchy of truths, the history of salvation, taught by the scriptures, then the teachings of the Gospel in the form of the creed, sacraments commandents and prayer.
Thus, when we teach the Gospel in this form, the ONLY form it can be taught and learned, then we are teaching the entire Gospel, the Gospel the apostles taught and preached. So when a local Catechism is taught, then the Gospel is being communicated.